Dropout presents a major challenge for causal inference in longitudinal studies with time-varying treatments. We focus on selective eligibility, an important but overlooked source of nonignorable dropout that occurs when a unit’s prior treatment history affects its eligibility for future treatments. Our motivating application evaluates a pretrial risk assessment instrument in the criminal justice system, where cases were randomly assigned to receive a risk assessment report. Selective eligibility arises because individuals can be rearrested over time, and rearrest depends on prior judicial decisions, which may be influenced by earlier treatment assignments. We develop a general methodological framework for longitudinal causal inference under selective eligibility. By conditioning on subgroups of units who would remain eligible for treatment under a given treatment history, we define time-specific eligible treatment effects and the expected total outcome under a given treatment sequence. Assuming a generalized form of sequential ignorability, we derive nonparametric identification formulas and the efficient influence functions for both estimands, yielding doubly robust estimators. Applying this methodology, we find that risk assessment reports increase alignment between judicial decisions and algorithmic recommendations, particularly when reports are provided repeatedly. However, the reports have a limited impact on downstream criminal justice outcomes.